1864] Prof. Cayley — Sextactic Points of a Plane Curve. 553 



station, p, was visited [and, from a height of 1100 feet, the summits v, r, 

 (Ty ^, and TT were observed projected against the sky, and o against other 

 mountains]. On the 21st, after having ridden out a heavy gale, they 

 succeeded in climbing Mount Walrus [marked tt], a mountain 1100 feet 

 high, surrounded by glaciers, and laid down as an island on the existing 

 charts. [From this mountain the station marked X in Mr. Chydenius's 

 map (Royal Society Proceedings, vol. xii. Plate IV.) was seen.] 



"Proceeding in the boats they reached, on the 22nd, and ascended a 

 mountain 2500 feet high, situated near the channel which joins the Stor- 

 fjord with the southern opening of Hinlopen Straits. This was named 

 White Mountain [and is marked v on the Map]. From this summit they 

 saw on a clear bright day the South Cape of North-east Land (/x). Mount 

 Loven about the middle of Hinlopen Straits on the west shore, and the 

 station marked <c on the eastern shore. Having thus ascertained satisfac- 

 tory points in the Storfjord, they proceeded again to the west coast of 

 Spitzbergen, with the intention of pushing to the northward as far as 

 possible, but had not proceeded far when they fell in with several boats 

 with the crews of wrecked sealing vessels. Of course they were obliged 

 to take these men on board ; and being short of provisions for the increased 

 number of hands, and the season drawing towards its close, they put back 

 to Tromsoe. The sealing vessels had been wrecked on the east side of 

 North-East Land, having got there by the north of the island. The men 

 had afterwards made their way in the boats through Hinlopen Straits, 

 having thus circumnavigated North-East Land — a feat said never to have 

 been accomplished before. 



"The shores of the Storfjord are mountainous. The glens and valleys 

 between the ridges are for the most part filled by glaciers, especially on 

 the western shore. The mountains average from 1000 to 1500 feet in 

 height, and belong in general to the Jura formation, which is here and 

 there broken through by basaltic rocks (hyperite). In the Jara have been 

 found skeletons, though not complete, of an Ichthyosaurus, closely resem- 

 bling the species found in Arctic America by Sir Edward Belcher's Expe- 

 dition. Mr. Malmgren, of the University of Helsingfors in Finland, 

 accompanied the Expedition in the capacity of zoologist." 



III. " On the Sextactic Points of a Plane Curve.^^ By A. Cayley, 

 F.R.S., Sadlerian Professor of Mathematics, Cambridge. Re- 

 ceived November 6, 1864. 



(Abstract.) 



It is, in my memoir '* On the Conic of Five-pointic Contact at any Point 

 of a Plane Curve " (Phil. Trans, vol. cxlix. (1859) pp. 371-400), remarked 

 that as in a plane curve there are certain singular points, viz. the points of 

 inflexion, where three consecutive points lie in a line, so there are singular 



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